Non-sinusoidal as in PWM, or peaks of current drawn from AC line by VFD or SMPS.

DC is simple, if a constant. And sine wave, RMS value same power as DC of the same number. "RMS" means Root Mean Squared, so the Squared term weights higher values more heavily. Distorted sine waves typically cause power power dissipation in wires and fuses for the same power delivered.

Wires take a long time to heat significantly, except at high multiples of rated current.

I've tested breakers, e.g. 20A rating with 30A worth of space heaters. That took 10 or 20 minutes. Depends on ambient temperature and air circulation, as well.

Wire insulation does get cooked eventually with such overload. But the rules of 15A breaker for 14 awg, 20A for 12 awg, 30A for 10 awg, which are overly conservative, probably prevent that. Good for outlets consumers can overload, as opposed to dedicated circuits.